Finite Group Databasebeta

← #30604356

Subgroups — #30604356

Order 15616.

424 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461074C211yesmaximal, characteristic
2#21461058C211yesmaximal, characteristic
3#21460764C212yesmaximal, complemented
4#21460764C212yesmaximal, complemented
5#21451166C211yesmaximal, characteristic
6#16840779—21no—
7#16840733—21no—
8#16840608—21no—
9#16840606—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×C4×C22⋊D61C2211yescharacteristic
13#16839695—21no—
14#16839684—21no—
15#16839643—21no—
16#16839641C411yescharacteristic
17#16839641C411yescharacteristic
18#16839635C2211yescharacteristic
19#16839635C2211yescharacteristic
20#16839633—21no—
21#16839622C411yescharacteristic
22C22×C4⋊C4×C61C411yescharacteristic
23C2×#11758213—41no—
24#14519844—41no—
25#14519834—41no—
26C22⋊#92420—22no—
27C22⋊#92420—22no—
28C4×#92420—41no—
29C22×C22⋊D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C4×C22⋊D61—41no—
32C4×C22⋊D61—41no—
33C2×C4⋊Dic61—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61C2×C411yescharacteristic
38C2×C22⋊Dic61C2×C411yescharacteristic
39C2×C22⋊Dic61C2311yescharacteristic
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C23×C4×C61C2×C411yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—41no—
55C2×C4⋊C4×C61—41no—
56C24×C61C22×C411yescharacteristic
57C23×D61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—42no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—81no—
66C22×C4×C61—81no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C2×C22⋊D61—22no—
70C2×C22⋊D61—22no—
71C2×C22⋊D61—41no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—81no—
80C2×#92420—42no—
81C2×#92420—42no—
82#11758213—82no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C22⋊Dic61—22no—
87C22⋊Dic61—22no—
88C22⋊Dic61—41no—
89#11758198—41no—
90#11758198—42no—
91#11758198—81no—
92C4⋊Dic61—81no—
93#11758196—41no—
94#11758196—42no—
95#11758196—81no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61C2×C22⋊C411yescharacteristic
103C23×C61#13112yes—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—41no—
108C22×D61—41no—
109C2×C4×C61—22no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—42no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—42no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—81no—
121C2×C4×C61—81no—
122C2×C4×C61—82no—
123C2×C4×C61#9911yescharacteristic
124C2×C4×C61#9911yescharacteristic
125C22⋊D61—44no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61#10112yes—
139C4×D61—42no—
140C4×D61—81no—
141#92420—82no—
142#92420—82no—
143#11577—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—22no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61#40811yescharacteristic
152C22×C61C2×#9911yescharacteristic
153C22×C61C2×#10111yescharacteristic
154C2×D61—42no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—81no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—42no—
162C4×C61—41no—
163C4×C61—81no—
164Dic61—22no—
165Dic61—41no—
166Dic61—41no—
167Dic61—81no—
168Dic61—81no—
169#2579—611no—
170#1465—611no—
171#1460—611no—
172#1326—612no—
173#1326—612no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61—42no—
177C2×C61#147211yescharacteristic
178C2×C61#212011yescharacteristic
179C2×C61#212111yescharacteristic
180D61—81no—
181C2×C4×D4—611no—
182C22×C4⋊C4#692311yescharacteristic
183#431—1221no—
184#407—1221no—
185#398—1221no—
186#396—1221no—
187#387—1221no—
188#386—611no—
189#386—611no—
190#385—611no—
191#385—611no—
192#385—1221no—
193#380—611no—
194#324—1221no—
195#323—612no—
196#323—612no—
197#323—1221no—
198C61#1157711yescharacteristic, complemented, Sylow
199C22×D4—611no—
200C23×C4—611no—
201C23×C4C2×#692311yescharacteristic
202C23×C4C2×#692311yescharacteristic
203C23×C4C2×#692311yescharacteristic
204C2×M16—2441no—
205C4×D4—2441no—
206C4×D4—2441no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—611no—
218C2×C22⋊C4—611no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C42—611no—
222C4⋊C8—2441no—
223C22⋊C8—1222no—
224C22⋊C8—1222no—
225C22⋊C8—2441no—
226C4×C8—2441no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232C24—611no—
233C24C22×#692311yescharacteristic
234C2×D4—1222no—
235C2×D4—1222no—
236C2×D4—2441no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—4881no—
254C22×C4C22⋊#692311yescharacteristic
255C22×C4C22⋊#692311yescharacteristic
256M16—4882no—
257C2×C8—2442no—
258C2×C8—2442no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—4881no—
263C4⋊C4—4881no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C22⋊C4—1222no—
267C22⋊C4—1222no—
268C22⋊C4—4881no—
269C22⋊C4—2441no—
270C22⋊C4—2442no—
271C22⋊C4—2441no—
272C42—1221no—
273C42—1221no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—1221no—
279C23—1221no—
280C23—1221no—
281C23—2441no—
282C23—2441no—
283C23C2×C22⋊#692311yescharacteristic
284C23#1451986512yes—
285D4—2444no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—612no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—4881no—
306C2×C4—2442no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4#1451983511yescharacteristic
316C2×C4#1451983511yescharacteristic
317C8—4882no—
318C8—4882no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—42no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—4881no—
327C22—2442no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22#1684073711yescharacteristic
332C22C2×#1451983511yescharacteristic
333C22D61⋊#10111yescharacteristic
334C4—21no—
335C4—21no—
336C4—42no—
337C4—41no—
338C4—81no—
339C4—1222no—
340C4—4881no—
341C4—4881no—
342C4—2441no—
343C4—2441no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—4881no—
348C2#2146109911yescharacteristic
349C2#2146207011yescharacteristic
350C2#2146207411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11577
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21460764C2semidirect
4. #21460764C2semidirect
198. C61#11577semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214610742
#214610582
#214607642
#214511662
#1157761